On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations
arXiv:2102.07376 · doi:10.1007/s42985-021-00126-3
Abstract
We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.
References in corpus (22)
- An integrable shallow water equation with peaked solitons
- Review of Summation-by-parts schemes for initial-boundary-value problems
- Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations
- Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
- Summation-by-parts operators for correction procedure via reconstruction
- A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
- PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems
- Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems
- General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
- Relaxation Runge-Kutta Methods for Hamiltonian Problems
- Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
- Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods
- Generalised Summation-by-Parts Operators and Variable Coefficients
- A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
- Entropy-stable, high-order summation-by-parts discretizations without interface penalties
- A conservative fully-discrete numerical method for the regularised shallow water wave equations
- Mimetic Properties of Difference Operators: Product and Chain Rules as for Functions of Bounded Variation and Entropy Stability of Second Derivatives
- Shock Dynamics in Layered Periodic Media
- Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients
- Solitary water waves created by variations in bathymetry
- Error boundedness of Correction Procedure via Reconstruction / Flux Reconstruction
- On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations